RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2018-07-10_23:31
(no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500)
Bits used mean chisqr p-value
1 to 24 15.82 23.8505 0.876446
2 to 25 15.69 19.1408 0.679491
3 to 26 15.42 28.1878 0.957208
4 to 27 15.31 27.4746 0.948535
5 to 28 15.63 22.5173 0.834366
6 to 29 15.54 32.9475 0.988554
7 to 30 15.46 21.8963 0.811260
8 to 31 15.62 13.5956 0.304506
9 to 32 15.90 9.5916 0.080143
Chisquare degrees of freedom: 17
---------------------------------------------------------------
p-value for KStest on those 9 p-values: 0.013221
Tough bday spacings test for dh-ranFile-2018-07-10_23:31: 4096 birthdays, year=2^32 days
Table of Expected vs. Observed counts:
Duplicates 0 1 2 3 4 5 6 7 8 9 >=10
Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1
Observed 7 36 76 94 102 84 51 31 13 4 2
(O-E)^2/E 0.5 0.0 0.1 0.1 0.2 0.4 0.0 0.1 0.2 1.0 1.0
Birthday Spacings: Sum(O-E)^2/E= 3.786, p= 0.044
RESULTS OF GCD FOR dh-ranFile-2018-07-10_23:31
Euclid's algorithm:
p-value, steps to gcd: 0.015045
p-value, dist. of gcd's: 0.274655
Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2018-07-10_23:31:
Note: lengthy test---for example, ~20 minutes for 850MHz PC
Bits 0 to 7---> 0.071 0.151 0.818 0.247 0.589 0.642 0.067 0.912
Bits 8 to 15---> 0.799 0.458 0.696 0.938 0.544 0.667 0.450 0.411
Bits 16 to 23---> 0.576 0.022 0.509 0.739 0.439 0.369 0.916 0.932
Bits 24 to 31---> 0.146 0.231 0.516 0.692 0.668 0.809 0.362 0.670
KS test for the above 32 p values: 0.330
The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2018-07-10_23:31,
p-values for 5 runs: 0.7848, 0.8934, 0.3826, 0.7896, 0.9554
Rank test for binary matrices (31x31) for dh-ranFile-2018-07-10_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=28 202 211.4 0.420 0.420
r= 29 4993 5134.0 3.873 4.293
r= 30 23400 23103.0 3.817 8.109
r= 31 11405 11551.5 1.859 9.968
chi-square = 9.968 with df = 3; p-value = 0.981
--------------------------------------------------------------
Rank test for binary matrices (32x32) for dh-ranFile-2018-07-10_23:31
RANK OBSERVED EXPECTED (O-E)^2/E SUM
r<=29 197 211.4 0.983 0.983
r= 30 5136 5134.0 0.001 0.984
r= 31 23004 23103.0 0.425 1.409
r= 32 11663 11551.5 1.076 2.484
chi-square = 2.484 with df = 3; p-value = 0.522
--------------------------------------------------------------
Rank test for binary matrices (6x8) for dh-ranFile-2018-07-10_23:31
b-rank test for bits 1 to 8, p=0.89579
b-rank test for bits 2 to 9, p=0.76838
b-rank test for bits 3 to 10, p=0.04147
b-rank test for bits 4 to 11, p=0.59273
b-rank test for bits 5 to 12, p=0.15333
b-rank test for bits 6 to 13, p=0.86933
b-rank test for bits 7 to 14, p=0.70385
b-rank test for bits 8 to 15, p=0.96203
b-rank test for bits 9 to 16, p=0.98295
b-rank test for bits 10 to 17, p=0.79295
b-rank test for bits 11 to 18, p=0.82784
b-rank test for bits 12 to 19, p=0.28087
b-rank test for bits 13 to 20, p=0.88710
b-rank test for bits 14 to 21, p=0.04463
b-rank test for bits 15 to 22, p=0.52938
b-rank test for bits 16 to 23, p=0.09069
b-rank test for bits 17 to 24, p=0.07784
b-rank test for bits 18 to 25, p=0.94244
b-rank test for bits 19 to 26, p=0.48573
b-rank test for bits 20 to 27, p=0.47479
b-rank test for bits 21 to 28, p=0.59793
b-rank test for bits 22 to 29, p=0.29899
b-rank test for bits 23 to 30, p=0.04022
b-rank test for bits 24 to 31, p=0.43415
b-rank test for bits 25 to 32, p=0.21448
TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices
The above should be 25 uniform [0,1] random variables:
The KS test for those 25 supposed UNI's yields p = 0.586341
THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2018-07-10_23:31
(20 bits/word, 2097152 words 20 bitstreams. No. missing words
should average 141909.33 with sigma=428.00.)
----------------------------------------------------------------
BITSTREAM test results.
Bitstream No. missing words z-score p-value
1 140746 -2.72 0.003283
2 142357 1.05 0.852210
3 142209 0.70 0.758087
4 141271 -1.49 0.067925
5 142157 0.58 0.718594
6 141886 -0.05 0.478265
7 141393 -1.21 0.113836
8 142142 0.54 0.706649
9 141860 -0.12 0.454121
10 142497 1.37 0.915133
11 142249 0.79 0.786292
12 142321 0.96 0.831936
13 141881 -0.07 0.473613
14 142405 1.16 0.876590
15 142146 0.55 0.709857
16 141615 -0.69 0.245825
17 141912 0.01 0.502489
18 141889 -0.05 0.481057
19 141356 -1.29 0.098035
20 142436 1.23 0.890752
----------------------------------------------------------------
OPSO test for dh-ranFile-2018-07-10_23:31
Bits used No. missing words z-score p-value
23 to 32 142075 0.5713 0.716094
22 to 31 141907 -0.0080 0.496795
21 to 30 141783 -0.4356 0.331556
20 to 29 141618 -1.0046 0.157548
19 to 28 141639 -0.9322 0.175624
18 to 27 142162 0.8713 0.808198
17 to 26 141806 -0.3563 0.360804
16 to 25 141938 0.0989 0.539376
15 to 24 141512 -1.3701 0.085327
14 to 23 142019 0.3782 0.647349
13 to 22 142203 1.0127 0.844388
12 to 21 142134 0.7747 0.780749
11 to 20 141903 -0.0218 0.491293
10 to 19 142040 0.4506 0.673856
9 to 18 141896 -0.0460 0.481669
8 to 17 141395 -1.7736 0.038069
7 to 16 142298 1.3402 0.909917
6 to 15 141924 0.0506 0.520172
5 to 14 142015 0.3644 0.642213
4 to 13 142451 1.8678 0.969107
3 to 12 142370 1.5885 0.943915
2 to 11 142241 1.1437 0.873624
1 to 10 141584 -1.1218 0.130968
-----------------------------------------------------------------
OQSO test for dh-ranFile-2018-07-10_23:31
Bits used No. missing words z-score p-value
28 to 32 142233 1.0972 0.863720
27 to 31 141758 -0.5130 0.303982
26 to 30 141299 -2.0689 0.019277
25 to 29 141987 0.2633 0.603836
24 to 28 142060 0.5107 0.695236
23 to 27 141922 0.0429 0.517129
22 to 26 142067 0.5345 0.703493
21 to 25 142133 0.7582 0.775835
20 to 24 142240 1.1209 0.868838
19 to 23 141846 -0.2147 0.415009
18 to 22 141819 -0.3062 0.379725
17 to 21 141861 -0.1638 0.434932
16 to 20 141958 0.1650 0.565521
15 to 19 142266 1.2091 0.886678
14 to 18 142020 0.3752 0.646227
13 to 17 141869 -0.1367 0.445629
12 to 16 141966 0.1921 0.576169
11 to 15 141608 -1.0215 0.153519
10 to 14 141795 -0.3876 0.349171
9 to 13 142187 0.9413 0.826713
8 to 12 141987 0.2633 0.603836
7 to 11 142600 2.3413 0.990390
6 to 10 142455 1.8497 0.967824
5 to 9 142191 0.9548 0.830164
4 to 8 142114 0.6938 0.756095
3 to 7 142171 0.8870 0.812465
2 to 6 142034 0.4226 0.663710
1 to 5 142063 0.5209 0.698787
-----------------------------------------------------------------
DNA test for dh-ranFile-2018-07-10_23:31
Bits used No. missing words z-score p-value
31 to 32 142089 0.5300 0.701944
30 to 31 142373 1.3678 0.914306
29 to 30 141953 0.1288 0.551250
28 to 29 141782 -0.3756 0.353605
27 to 28 141893 -0.0482 0.480790
26 to 27 141507 -1.1868 0.117650
25 to 26 141445 -1.3697 0.085390
24 to 25 141869 -0.1190 0.452651
23 to 24 141373 -1.5821 0.056814
22 to 23 141596 -0.9243 0.177671
21 to 22 141484 -1.2547 0.104801
20 to 21 142309 1.1790 0.880794
19 to 20 141393 -1.5231 0.063867
18 to 19 141847 -0.1839 0.427060
17 to 18 141895 -0.0423 0.483141
16 to 17 141774 -0.3992 0.344872
15 to 16 141485 -1.2517 0.105338
14 to 15 142420 1.5064 0.934018
13 to 14 141946 0.1082 0.543070
12 to 13 142475 1.6686 0.952406
11 to 12 141706 -0.5998 0.274322
10 to 11 142056 0.4327 0.667367
9 to 10 141690 -0.6470 0.258819
8 to 9 142823 2.6952 0.996483
7 to 8 142002 0.2734 0.607713
6 to 7 142050 0.4150 0.660913
5 to 6 141739 -0.5024 0.307676
4 to 5 142147 0.7011 0.758377
3 to 4 141366 -1.6027 0.054496
2 to 3 142457 1.6155 0.946904
1 to 2 141841 -0.2016 0.420129
-----------------------------------------------------------------
Test result COUNT-THE-1's in bytes for dh-ranFile-2018-07-10_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 2560000)
chisquare z-score p-value
2426.32 -1.042 0.148699
Test results for specific bytes for dh-ranFile-2018-07-10_23:31
(Degrees of freedom: 5^4-5^3=2500; sample size: 256000)
bits used chisquare z-score p-value
1 to 8 2448.46 -0.729 0.233047
2 to 9 2494.01 -0.085 0.466232
3 to 10 2417.28 -1.170 0.121046
4 to 11 2439.35 -0.858 0.195541
5 to 12 2396.10 -1.469 0.070873
6 to 13 2384.18 -1.638 0.050721
7 to 14 2585.44 1.208 0.886528
8 to 15 2540.97 0.579 0.718860
9 to 16 2462.21 -0.534 0.296538
10 to 17 2538.02 0.538 0.704612
11 to 18 2482.16 -0.252 0.400412
12 to 19 2530.18 0.427 0.665256
13 to 20 2434.71 -0.923 0.177910
14 to 21 2496.76 -0.046 0.481749
15 to 22 2546.29 0.655 0.743629
16 to 23 2539.57 0.560 0.712136
17 to 24 2549.61 0.702 0.758542
18 to 25 2552.14 0.737 0.769542
19 to 26 2397.44 -1.450 0.073467
20 to 27 2608.23 1.531 0.937071
21 to 28 2615.40 1.632 0.948668
22 to 29 2448.09 -0.734 0.231425
23 to 30 2355.88 -2.038 0.020770
24 to 31 2447.07 -0.749 0.227060
25 to 32 2541.73 0.590 0.722451
CDPARK for dh-ranFile-2018-07-10_23:31: result of 10 tests
(Of 12000 tries, the average no. of successes should be
3523.0 with sigma=21.9)
No. succeses z-score p-value
3547 1.0959 0.863437
3501 -1.0046 0.157553
3535 0.5479 0.708135
3525 0.0913 0.536383
3502 -0.9589 0.168804
3545 1.0046 0.842447
3494 -1.3242 0.092718
3492 -1.4155 0.078457
3531 0.3653 0.642555
3493 -1.3699 0.085365
Square side=100, avg. no. parked=3516.50 sample std.=21.16
p-value of the KSTEST for those 10 p-values: 0.315397
Results for the MINIMUM DISTANCE test for dh-ranFile-2018-07-10_23:31
0.1274,0.4338,0.6432,0.3297,0.6578,0.2912,0.5956,0.0929,0.9684,0.1316,
The KS test for those 10 p-values: 0.644663
The 3DSPHERES test for dh-ranFile-2018-07-10_23:31
sample no r^3 equiv. uni.
1 27.386 0.598626
2 6.037 0.182278
3 44.128 0.770287
4 1.738 0.056297
5 11.774 0.324615
6 30.269 0.635410
7 8.665 0.250870
8 50.417 0.813734
9 6.966 0.207213
10 8.904 0.256808
11 10.059 0.284867
12 57.899 0.854847
13 87.149 0.945250
14 74.424 0.916325
15 44.673 0.774424
16 7.726 0.227032
17 25.023 0.565742
18 8.586 0.248880
19 15.517 0.403833
20 34.449 0.682822
--------------------------------------------------------------
p-value for KS test on those 20 p-values: 0.844919
RESULTS OF SQUEEZE TEST FOR dh-ranFile-2018-07-10_23:31
Table of standardized frequency counts
(obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...)
1.3 1.3 0.1 -1.3 0.3 -1.5
0.1 1.4 -0.9 -0.5 0.8 -0.5
-1.1 1.3 -1.1 -1.2 0.2 2.0
-0.4 0.4 -0.8 -0.4 1.1 0.5
-0.8 0.1 1.1 0.2 -0.8 -0.7
0.4 -1.7 0.8 0.5 -1.9 0.2
-0.2 2.1 1.3 -0.7 0.1 1.0
0.8
Chi-square with 42 degrees of freedom:42.493107
z-score=0.053802, p-value=0.550270
_____________________________________________________________
Results of the OSUM test for dh-ranFile-2018-07-10_23:31
Test no p-value
1 0.219722
2 0.126412
3 0.013665
4 0.187106
5 0.811632
6 0.904301
7 0.116340
8 0.047366
9 0.622945
10 0.115486
_____________________________________________________________
p-value for 10 kstests on 100 sums: 0.025938
Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2018-07-10_23:31:
(for k>=2, the prob. of a run of length k is 2*k/(k+1)!)
Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E
2 66666.67 66749 0.10 66534 0.26
3 25000.00 24930 0.20 25079 0.25
4 6666.67 6604 0.59 6693 0.10
5 1388.89 1417 0.57 1412 0.38
6 238.10 253 0.93 243 0.10
7 34.72 39 0.53 32 0.21
8 4.96 7 0.84 6 0.22
p=0.29026 p=0.04282
Number of rngs required: 687652, p-value: 0.193
RESULTS OF CRAPS TEST for dh-ranFile-2018-07-10_23:31
No. of wins: Observed Expected
98266 98585.9
z-score=-1.431, pvalue=0.07627
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66314 66666.7 1.866 1.866
2 37890 37654.3 1.475 3.341
3 26899 26954.7 0.115 3.456
4 19214 19313.5 0.512 3.968
5 13925 13851.4 0.391 4.359
6 9784 9943.5 2.560 6.919
7 7202 7145.0 0.454 7.373
8 5256 5139.1 2.660 10.034
9 3725 3699.9 0.171 10.204
10 2700 2666.3 0.426 10.630
11 1962 1923.3 0.778 11.408
12 1427 1388.7 1.054 12.462
13 982 1003.7 0.470 12.932
14 721 726.1 0.036 12.968
15 518 525.8 0.117 13.085
16 401 381.2 1.034 14.119
17 280 276.5 0.043 14.162
18 219 200.8 1.644 15.806
19 173 146.0 4.999 20.805
20 122 106.2 2.346 23.151
21 286 287.1 0.004 23.155
Chisq= 23.16 for 20 degrees of freedom, p= 0.71877
SUMMARY of craptest
p-value for no. of wins: 0.076273
p-value for throws/game: 0.718774
_____________________________________________________________
RESULTS OF CRAPS TEST2 for dh-ranFile-2018-07-10_23:31
No. of wins: Observed Expected
98728 98585.9
z-score= 0.636, pvalue=0.73753
Analysis of Throws-per-Game:
Throws Observed Expected Chisq Sum of (O-E)^2/E
1 66755 66666.7 0.117 0.117
2 37685 37654.3 0.025 0.142
3 27293 26954.7 4.245 4.387
4 19151 19313.5 1.367 5.754
5 13731 13851.4 1.047 6.801
6 9949 9943.5 0.003 6.804
7 7163 7145.0 0.045 6.849
8 4978 5139.1 5.048 11.897
9 3754 3699.9 0.792 12.689
10 2627 2666.3 0.579 13.269
11 1823 1923.3 5.234 18.502
12 1351 1388.7 1.026 19.528
13 1050 1003.7 2.134 21.662
14 725 726.1 0.002 21.664
15 542 525.8 0.497 22.161
16 357 381.2 1.530 23.691
17 304 276.5 2.727 26.418
18 207 200.8 0.190 26.607
19 159 146.0 1.160 27.768
20 105 106.2 0.014 27.782
21 291 287.1 0.053 27.834
Chisq= 27.83 for 20 degrees of freedom, p= 0.88662
SUMMARY of craptest
p-value for no. of wins: 0.737527
p-value for throws/game: 0.886622
_____________________________________________________________
***** TEST SUMMARY *****
All p-values:
0.0033,0.0132,0.0137,0.0150,0.0193,0.0208,0.0218,0.0259,0.0381,0.0402,
0.0415,0.0428,0.0435,0.0446,0.0474,0.0507,0.0545,0.0563,0.0568,0.0639,
0.0666,0.0679,0.0709,0.0711,0.0735,0.0763,0.0778,0.0785,0.0801,0.0853,
0.0854,0.0854,0.0907,0.0927,0.0929,0.0980,0.1048,0.1053,0.1138,0.1155,
0.1163,0.1177,0.1210,0.1264,0.1274,0.1310,0.1316,0.1463,0.1487,0.1514,
0.1533,0.1535,0.1575,0.1576,0.1688,0.1756,0.1777,0.1779,0.1823,0.1871,
0.1925,0.1955,0.2072,0.2145,0.2197,0.2270,0.2271,0.2307,0.2314,0.2330,
0.2458,0.2470,0.2489,0.2509,0.2568,0.2588,0.2743,0.2747,0.2809,0.2849,
0.2903,0.2912,0.2965,0.2990,0.3040,0.3045,0.3077,0.3154,0.3246,0.3297,
0.3303,0.3316,0.3449,0.3492,0.3536,0.3608,0.3618,0.3692,0.3797,0.3826,
0.4004,0.4038,0.4109,0.4150,0.4201,0.4271,0.4338,0.4341,0.4349,0.4393,
0.4456,0.4501,0.4527,0.4541,0.4576,0.4662,0.4736,0.4748,0.4783,0.4808,
0.4811,0.4817,0.4817,0.4831,0.4857,0.4913,0.4968,0.5025,0.5094,0.5161,
0.5171,0.5202,0.5219,0.5294,0.5364,0.5394,0.5431,0.5437,0.5503,0.5513,
0.5655,0.5657,0.5758,0.5762,0.5863,0.5886,0.5927,0.5956,0.5979,0.5986,
0.6038,0.6038,0.6077,0.6229,0.6354,0.6420,0.6422,0.6426,0.6432,0.6447,
0.6462,0.6473,0.6578,0.6609,0.6637,0.6653,0.6670,0.6674,0.6683,0.6697,
0.6739,0.6795,0.6828,0.6917,0.6952,0.6962,0.6988,0.7019,0.7035,0.7038,
0.7046,0.7066,0.7081,0.7099,0.7121,0.7161,0.7186,0.7188,0.7189,0.7225,
0.7375,0.7386,0.7436,0.7561,0.7581,0.7584,0.7585,0.7684,0.7695,0.7703,
0.7744,0.7758,0.7807,0.7848,0.7863,0.7896,0.7929,0.7992,0.8082,0.8092,
0.8113,0.8116,0.8125,0.8137,0.8179,0.8267,0.8278,0.8302,0.8319,0.8344,
0.8424,0.8444,0.8449,0.8522,0.8548,0.8634,0.8637,0.8688,0.8693,0.8736,
0.8764,0.8766,0.8808,0.8865,0.8866,0.8867,0.8871,0.8908,0.8934,0.8958,
0.9043,0.9099,0.9124,0.9143,0.9151,0.9163,0.9164,0.9325,0.9340,0.9371,
0.9385,0.9424,0.9439,0.9453,0.9469,0.9485,0.9487,0.9524,0.9554,0.9572,
0.9620,0.9678,0.9684,0.9691,0.9812,0.9830,0.9886,0.9904,0.9965,
Overall p-value after applying KStest on 269 p-values = 0.256109
In response to requests, we have provided a list of all the p-values
produced by the tests you have chosen for this run. The individual
p-values are supposed to be uniform in [0,1), but they are not necessarily
independent. So even though we have applied a KSTEST to the accumulated
p-values, the result is not necessarily---even if your file contains truly
random bits---uniform in [0,1). But it is probably pretty close, so take
that last p-value with a grain of salt. In particular, there may be some
values so close to 0 or 1 that the tests they came from should be applied
several more times, or new, related tests should be undertaken.